Are they any good tutorials on how to make animated mud/dirt?
There are a ton of fluid simulation tutorials that can get you started. You're going to want a high viscosity fluid to emulate mud. You could then set up your machine to be a collider in the simulation.
Here is a tutorial that covers the basics of fluid simulation.
You could also augment your simulation with creative use of metaballs and particles.
Here is a simple tutorial that covers the very basics of metaballs
Here is a more advanced tutorial that covers metaballs and particles
Finally, here are a couple more fluid simulation tutorials:
Create Splashes in Blender
Realistic Fluid Simulation